d^2+11d+16=0

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Solution for d^2+11d+16=0 equation:


Simplifying
d2 + 11d + 16 = 0

Reorder the terms:
16 + 11d + d2 = 0

Solving
16 + 11d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 11d + -16 + d2 = 0 + -16

Reorder the terms:
16 + -16 + 11d + d2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 11d + d2 = 0 + -16
11d + d2 = 0 + -16

Combine like terms: 0 + -16 = -16
11d + d2 = -16

The d term is 11d.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11d + 30.25 + d2 = -16 + 30.25

Reorder the terms:
30.25 + 11d + d2 = -16 + 30.25

Combine like terms: -16 + 30.25 = 14.25
30.25 + 11d + d2 = 14.25

Factor a perfect square on the left side:
(d + 5.5)(d + 5.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(d + 5.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

d + 5.5 = 3.774917218 Simplifying d + 5.5 = 3.774917218 Reorder the terms: 5.5 + d = 3.774917218 Solving 5.5 + d = 3.774917218 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + d = 3.774917218 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + d = 3.774917218 + -5.5 d = 3.774917218 + -5.5 Combine like terms: 3.774917218 + -5.5 = -1.725082782 d = -1.725082782 Simplifying d = -1.725082782

Subproblem 2

d + 5.5 = -3.774917218 Simplifying d + 5.5 = -3.774917218 Reorder the terms: 5.5 + d = -3.774917218 Solving 5.5 + d = -3.774917218 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + d = -3.774917218 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + d = -3.774917218 + -5.5 d = -3.774917218 + -5.5 Combine like terms: -3.774917218 + -5.5 = -9.274917218 d = -9.274917218 Simplifying d = -9.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. d = {-1.725082782, -9.274917218}

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